OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
The enumeration of these partitions by sum is given by A325766.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
12: {1,1,2}
18: {1,2,2}
36: {1,1,2,2}
60: {1,1,2,3}
120: {1,1,1,2,3}
180: {1,1,2,2,3}
360: {1,1,1,2,2,3}
450: {1,2,2,3,3}
540: {1,1,2,2,2,3}
600: {1,1,1,2,3,3}
840: {1,1,1,2,3,4}
1260: {1,1,2,2,3,4}
1350: {1,2,2,2,3,3}
1500: {1,1,2,3,3,3}
1680: {1,1,1,1,2,3,4}
1800: {1,1,1,2,2,3,3}
2250: {1,2,2,3,3,3}
2520: {1,1,1,2,2,3,4}
MATHEMATICA
red[n_]:=If[n==1, 1, Times@@Prime/@Last/@FactorInteger[n]];
Select[Range[1000], #==1||Range[PrimeNu[#]]==PrimePi/@First/@FactorInteger[#]&&Divisible[#, red[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 19 2019
STATUS
approved